**MSC2020** 78-10

### Mathematical modeling of the magnetic properties of axisymmetric hard superconductors of the second kind in the Kim model

#### N. D. Kuzmichev^{1}, A. A. Shushpanov^{2}, M. A. Vasyutin^{3}

Annotation | Authors perform mathematical modeling of magnetic properties, such as current distribution, intrinsic magnetic field and magnetization of a number of axisymmetric superconductors of the second kind, for example, of a sphere with the dependence of the critical current density on the local magnetic field in the Kim model. The simulation is based on equation that is integral with respect to coordinate and differential with respect to time. The equation describes time evolution of the critical current density and is solved numerically for a uniformly varying external magnetic field. The shape of the sample is set using a distorted rectangular irregular mesh with compaction to the edges of the sample. While solving the equation of current motion, the total magnetic field iscalculated at the points of the superconductor to calculate the value of the critical current density. In the article, the obtained solutions are used to visualize the current distribution in the volume of a superconductor and to construct magnetization hysteresis loops. Also, thanks to the calculations of the magnetic field in the center of the sample, the dependencies of the total penetration field for samples with different aspect ratios are obtained. |
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Keywords | magnetization, hard II-type superconductors, Kim model, axisymmetric body, integrodifferential equation, hysteresis loop |

^{1}**Nikolay D. Kuzmichev**, Professor of Department of Design and Technology Informatics, Mordovia State University (68 Bolshevistskaya St., Saransk 430005, Russia), Dr. Sci.(Physics and Mathematics), ORCID: http://orcid.org/0000-0001-6707-4950, kuzmichevnd@yandex.ru^{2}**Aleksey A. Shushpanov**, Post-Graduate Student of Department of Applied Mathematics, Differential \Equations and Theoretical Mechanics, Mordovia State University (68 Bolshevistskaya St., Saransk 430005,Russia), ORCID: http://orcid.org/0000-0002-5005-9831, aashushpanov@gmail.com^{3}**Mihail A. Vasyutin**, Associate Professor of Department of Design and Technology Informatics, Mordovia State University (68 Bolshevistskaya St., Saransk 430005, Russia), Ph. D. (Physics and Mathematics), ORCID: http://orcid.org/0000-0002-4856-7407, vasyutinm@mail.ru

**Citation**: N. D. Kuzmichev, A. A. Shushpanov, M. A. Vasyutin, "[Mathematical modeling of the magnetic properties of axisymmetric hard superconductors of the second kind in the Kim model]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,22:4 (2020) 456–462 (In Russian)

**DOI** 10.15507/2079-6900.22.202004.456-462